Wind Turbine Power Output Formula

Wind Turbine Power Equation:

\[ P = 0.5 \times \rho \times A \times v^3 \times C_p \]

Air Density (ρ):

kg/m³

Swept Area (A):

m²

Wind Speed (v):

m/s

Power Coefficient (Cp):

(0-0.59)

Wind Turbine Power Output (P):

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1. What is the Wind Turbine Power Output Formula?

The Wind Turbine Power Output Formula calculates the theoretical maximum power that can be extracted from wind by a turbine. It is based on the kinetic energy of moving air and the efficiency of the turbine in converting this energy to mechanical power.

2. How Does the Calculator Work?

The calculator uses the wind power equation:

\[ P = 0.5 \times \rho \times A \times v^3 \times C_p \]

Where:

\( P \) — Power output in watts (W)
\( \rho \) — Air density in kg/m³
\( A \) — Swept area of turbine blades in m²
\( v \) — Wind speed in m/s
\( C_p \) — Power coefficient (Betz limit: 0.59 maximum)

Explanation: The equation shows that power output is proportional to the cube of wind speed, making wind speed the most critical factor in wind power generation.

3. Importance of Wind Power Calculation

Details: Accurate power calculation is essential for wind farm planning, turbine sizing, energy production forecasting, and economic feasibility studies of wind energy projects.

4. Using the Calculator

Tips: Enter air density (typically 1.225 kg/m³ at sea level), swept area (π × radius² for circular blades), wind speed, and power coefficient (typically 0.35-0.45 for modern turbines). All values must be positive.

5. Frequently Asked Questions (FAQ)

Q1: What is the Betz limit?
A: The Betz limit (59.3%) is the theoretical maximum efficiency for any wind turbine, representing the maximum fraction of wind kinetic energy that can be converted to mechanical energy.

Q2: Why is wind speed cubed in the formula?
A: Wind speed is cubed because kinetic energy is proportional to velocity squared, and the mass flow rate is proportional to velocity, resulting in v³ dependence.

Q3: What is typical air density for calculations?
A: Standard air density at sea level is 1.225 kg/m³, but it decreases with altitude and varies with temperature and pressure.

Q4: How do I calculate swept area?
A: For horizontal axis turbines, swept area A = π × r², where r is the blade length (radius of the circle swept by the blades).

Q5: What affects the power coefficient?
A: Power coefficient depends on blade design, angle of attack, tip speed ratio, and aerodynamic efficiency. Modern turbines achieve 35-45% efficiency.